A general framework of latent trait item response models for continuous responses is given. In contrast to classical test theory (CTT) models, which traditionally distinguish between true scores and error scores, the responses are clearly linked to latent traits. It is shown that CTT models can be derived as special cases, but the model class is…

Diagnostic tests are typically administered in a multiple-choice (MC) format due to their advantages of objectivity and time efficiency. The MC-deterministic input, noisy "and" gate (DINA) family of models, a representative class of cognitive diagnostic models for MC items, efficiently and parsimoniously estimates the mastery profiles of…